A New Approach to Rational Values of Trigonometric Functions
arXiv:0904.0826
Abstract
It is well known that sin(aπ/b), cos(aπ/b), etc., are only rational numbers for a few select integers a and b. We show that this is equivalent to the fact that only for d = 1,2,3,4, and 6 is the primitive dth root of unity of degree 2 over Q.
4 pages, 2 figures, 5 references, with new 6th reference to an easier proof of my result